Question

with details.

3. A large tank contains 800 gal of water in which 42 lb of salt are dissolved. Brine containing 2 lb of of dissolved salt per gal is pumped into the tank at a rate of 4 gal per minute, and the mixture, kept uniform by stirring, is pumped out at the same rate. (a) Find the amount x(t) of salt in the tank, at time t. (b) How long will it take for the amount of salt in the tank to become 60 lb?

Answer 1

. . let us First consider the volume of boine as a functus of time vul Notice that we have 4 gallmen flowing en and a gal/min flowing out. Thus e = 4450 gal men Now using the fact that veo=8 - we know that volume after une + 3 ал е усне Яoo as rate of flowing out = rate of flowing on let tilb) be the amount of salt in pounds at time t t we know that we kno the concentration of what's coming in ý albisalen i Mone over z(t) ebligast is the concentracion of brine (salt water) that is leaving the tank aflime t e olet - ( amount of salt in) - l'amount of sceber ord KU) Vilt) Ko= 42 lbs Bedt 190 200 a 1600-Alt) On - both sedy J 1600-Act)

PNL, DIL 900 4101= 42 - 11 | 1600-86) = + o desen - 1800 - AW) = e .ee 1600-42 = e.elciec + Teº = 1550 1600-44 = 1o. 1558 + 1600 - 1552 e too = *-le) | 260= 1600 - 1550 è žoo 7 ② let after t.. minutes xlt) = 60 4 + 60 - 1600 - 1550 e Too + 1550 to 1600-60 = ether a 1540 + m2 too long tto -200 ( ) t o . 2.324 minutes after t= 20324 minutes amount of 1558 salto in the tank to become to lb
have a good day sir please like it thanks alot